Modelling of 3‐D Linear Viscoelastic Swelling of Charged Tissues and Gels

The skeleton of hydrated tissues or gels exhibits flow‐independent viscoelastic properties [2] which are strongly coupled with the dissipative phenomena resulting from the interstitial fluid flow and the electrochemical swelling mechanisms [4]. Following this, it is the goal of this contribution to combine a linear viscoelasticity formulation with an electrochemical swelling theory in the framework of a well‐founded multiphasic concept. Proceeding from a macroscopic mixture approach, the governing equations can be expressed in terms of three primary variables, namely the solid displacement u _S, the effective pore‐fluid pressure p and the molar salt concentration c_m of the interstitial fluid.     

Asymptotic Analysis of a Nonlinear Parabolic Problem Modelling Miscible Compressible Displacement in Porous Media

We study the asymptotic behavior, with respect to high Peclet numbers, of a model describing a compressible and miscible displacement in a porous medium. The transport of mass is then described by a nonlinear, fully coupled and degenerate parabolic system. Using non-classical estimates and renormalization tools, we prove existence of relevant weak solutions for the limit problem.      

Mass Transfer in Porous Media

In this contribution, a constitutive model based on the macromechanical Theory of Porous Media (TPM) for a saturated thermo elastic porous body has been developed. The body under investigation consists of an organic and inorganic moisturized phases and a gas phase. Based on a consistent thermomechanical treatment, the governing equations and constitutive equations will be given. Thus, we obtain a mathematical concept describing the motion of the solid phase, the pressure of the gas phase, the temperature of the mixture and the biodegradation of organic material into a gas mixture of methane and carbon dioxide produced by bacterial decomposition during stable methane fermentation (biogas). (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

多孔介质中可压缩流体力学方程组经典解的整体存在性与破裂现象

利用拟线性双曲型方程组极值原理,改进了HSIAO Ling和D.Serre得到的关于多孔介质中可压缩流体力学方程组解的存在性结果,给出了其Cauchy问题的一个关于经典解整体存在和破裂的完整结果．这些结果说明强耗散有助于“小”解的光滑性．     

Convective Instabilities in Anisotropic Porous Media

This paper addresses the problem of the onset of Rayleigh-Bénard convection in a porous layer using Brinkman's equation and anisotropic permeability. The critical Rayleigh number and wave number at marginal stabilities are calculated for both free and rigid boundaries. In both cases, it is noted that there exist ranges for which the stability criteria is intermediate to the low porosity Darcy approximation and to high porosity single viscous fluid. The permeability anisotropy is found to select the mode of instability.     

多孔介质中颗粒性态分析

分析了流经多孔介质的、充满颗粒材料的、混合液流动中的颗粒相性态.试图建立扩散和耗散过程模型,量化了在本征体积平均时出现的偏差项,从而导出流动方程.     

Liquid Flow in Partially Saturated Porous Media

We consider a picture for the filtration of a liquid in a partiallysaturated porous medium, leading to a two-phase one-dimensionalfree boundary problem of the following type: The liquid pressuresatisfies an elliptic equation in the saturated region and anon-linear parabolic equation in the unsaturated region, whilepressure and velocity are continuous across the interface. This scheme reduces to the study of the non-linear parabolicfree boundary problem in the unsaturated phase with cauchy dataprescribed on the free boundary, for such a problem existence,uniqueness and continuous dependence theorems are proved.     

Space-time DG Method for Porous Media

In this work we present a new coupled space-time discontinuous Galerkin method for the dynamical analysis of fully-saturated porous media. The method consists of a finite element discretization in space and time simultaneously. The numerical solution is solved on every time-slab (Qⁿ = Ω × ℐⁿ), which is in analogy to classical finite difference methods in time. The method is stable and efficient. The computational accuracy can be easily raised by increasing the order of the ansatz functions. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

微极性多组分多孔介质材料的混合物理论

将描述多组分系统的复合混合物理论与微极性连续介质力学理论相结合,建立了描述微极性多组分多孔介质材料的混合物理论.假定系统由多组分的微极性弹性固体和多组分微极性粘性流体组成.给出由混合物理论建立的系统的平衡方程.依据热力学第二定律以及本构假设建立了系统的本构方程,并使场方程闭合.为考虑固相的压缩性,在液相自由能函数中引入液相体积分数作为内变量,得到动力相容条件,用以限制固、液两相界面压力差的变化.最后,基于线性化理论得到线性化的本构方程和场方程,建立了考虑介质微极性的热-水力-力学组分输运模型.此理论框架可以运用到可变形多孔介质中污染物、药物以及农药输运等问题中,所得到的微极性多组分多孔介质系统的闭合场方程经退化后,可变为固、流相都为单一组分的多孔介质系统场方程,它与Eringen得到的结果一致.     

Dynamic Wave Propagation in Porous Media Semi-Infinite Domains

The problem of dynamic wave propagation in semi-infinite domains is of great importance, especially, in subjects of applied mechanics and geomechanics, such as the issues of earthquake wave propagation in an infinite half-space and soil-structure interaction under seismic loading. In such problems, the elastic waves are supposed to propagate to infinity, which requires a special treatment of the boundaries in initial boundary-value problems (IBVP). Saturated porous materials, e. g. soil, basically represent volumetrically coupled solid-fluid aggregates. Based on the continuum-mechanical principles and the established macroscopic Theory of Porous Media (TPM) [1, 2], the governing balance equations yield a coupled system of partial differential equations (PDE). Restricting the discussion to the isothermal and geometrically linear case, this system comprises the solid and fluid momentum balances and the overall volume balance, and can be conveniently treated numerically following an implicit monolithic approach [3]. Therefore, the equations are firstly discretised in space using the mixed Finite Element Method (FEM) together with quasi-static Infinite Elements (IE) at the boundaries that represent the extension of the domain to infinity [4], and secondly in time using an appropriate implicit time-integration scheme. Additionally, a stable implementation of the Viscous Damping Boundary (VDB) method [5] for the simulation of transient waves at infinity is presented, which implicitly treats the damping boundary terms in a weakly imposed sense. The proposed algorithm is implemented into the FE tool PANDAS and tested on a two-dimensional IBVP. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Uncertainty Quantification for Two-Phase Flow in Heterogeneous Porous Media

The simulation of flow and transport in porous media such as aquifers often involve dealing with complex heterogeneities. They are characterized by varying hydrogeological properties which differ strongly from the adjacent medium and often lead to significant changes of the flow behavior. However detailed information about the location of such heterogeneities is not always known. The deterministic models thus need to be extended stochastically to quantify uncertainties. As mathematical model we use the capillarity-free fractional flow formulation for two immiscible and incompressible fluid phases in a two-dimensional and partitioned domain. To cope with the randomly located heterogeneity interfaces we employ a stochastic Galerkin (SG) method [4]. The physical space of this system then is modelled by a central upwind finite volume scheme [5] in combination with mixed finite elements [7]. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parallel Solution Methods for Porous Media Models in Biomechanics

We present a biomechanical application of our parallel finite element model for coupled problems in solid mechanics. This programming framework provides a very lean and flexible interface, which allows to realize time-dependent nonlinear simulations. In this context, a special variant of a stabilized local Gauß-Seidel preconditioner is introduced, which can be successfully employed to large scale computations. Finally, the efficiency of the implemented algorithm is shown by a numerical example considering the axial compression of a L4-L5 motion segment of the spine. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

层状多孔介质中渗流湿峰的不稳定分析

在部分饱和与部分干的层状多孔介质中，建立了一维渗流问题的数学模型．在自然的条件下，证明了一类退化抛物方程弱解的存在唯一性．揭示了一个重要性质，即当下层介质的孔隙比上层更粗时，层状交界面具有隔水作用．这一作用将会在展状交界面不均匀时导致指状湿峰的出现．同时也说明，较粗孔隙的上层具有防止水分蒸发的作用．     

Coupled Problems of Dynamics in Materially Incompressible Saturated Porous Media

The mechanical behavior of saturated porous materials is largely governed by the interaction between the solid skeleton and the pore fluid. This interaction is particularly strong in dynamic problems and leads to numerical challenges especially in the case of incompressible constituents. In fact, the permeability plays a significant role in this coupling and influences the choice of a proper time integration scheme. Proceeding from the macroscopic Theory of Porous Media (TPM) within the isothermal and geometrical linear regime, the governing balance equations of the dynamic binary solid–fluid model are the solid and fluid momentum balances, and the overall volume balance of the biphasic mixture. This set of coupled partial differential equations (PDEs) is solved within the framework of the mixed Finite Element Method (FEM) applying two different time solution methods, viz., a monolithic implicit and a splitted implicit–explicit scheme. The time stepping algorithms are implemented into the FE program PANDAS and a Scilab FE routine and compared on a one–dimensional wave propagation example. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

饱水孔隙介质的质量耦合波动问题

本文按照混合物理论严格地推导出了饱和孔隙介质的一般波传播理论.该理论的重要性在于包含了质量耦合作用,并为研究该问题提供了理性基础和实用方程.本文对所得方程中的系数的物理意义和热力学限制进行了讨论.通过比较认为本文的理论和Biot古典理论基本上一致.本文还对完全透水、完全不透水和具有刚性固体骨架的介质的无边界条件下的波传播问题进行了研究,得到了一些有意义的结论.     

流体饱和多孔介质中波传播问题的有限元分析

采用基于混合物理论的多孔介质模型,给出流体饱和两相多孔介质波动问题的有限元分析方法·　采用罚方法导出的有限元动力方程,时间积分可采用显式和隐式积分两种方案·　用编制的有限元程序分析了一维柱体在跃阶载荷和脉冲载荷作用下的波传播问题,得到该两种瞬态载荷作用下固体和流体相位移、速度以及固体相有效应力和孔隙压力随时间的变化关系,并对波的传播现象进行了分析·　所得结果与理论相吻合·     

非牛顿幂律流体球向不定常渗流

本文研究了弱压缩非牛顿幂律流体球向不定常渗流,导出了抛物型偏微分非线性方程.球向扩散方程是其特殊情况.用Laplace变换的方法,找到了线性化后方程的解析解和渐近解.用影响半径的概念和平均值方法求得了近似解.渐近解和近似解的结构是相似的,从而丰富了非牛顿流体一维不定常渗流的理论.